The Fourier integral operators on Hardy spaces associated with Herz spaces

Lixia Liu; Bolin Ma; Sanyang Liu

Czechoslovak Mathematical Journal (2011)

  • Volume: 61, Issue: 1, page 271-287
  • ISSN: 0011-4642

Abstract

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In this paper, it is proved that the Fourier integral operators of order m , with - n < m ≤ - ( n - 1 ) / 2 , are bounded from three kinds of Hardy spaces associated with Herz spaces to their corresponding Herz spaces.

How to cite

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Liu, Lixia, Ma, Bolin, and Liu, Sanyang. "The Fourier integral operators on Hardy spaces associated with Herz spaces." Czechoslovak Mathematical Journal 61.1 (2011): 271-287. <http://eudml.org/doc/196328>.

@article{Liu2011,
abstract = {In this paper, it is proved that the Fourier integral operators of order $m$, with $-n < m \le -(n-1)/2$, are bounded from three kinds of Hardy spaces associated with Herz spaces to their corresponding Herz spaces.},
author = {Liu, Lixia, Ma, Bolin, Liu, Sanyang},
journal = {Czechoslovak Mathematical Journal},
keywords = {Fourier integral operator; Hardy spaces; Herz spaces; Fourier integral operator; Hardy space; Herz space},
language = {eng},
number = {1},
pages = {271-287},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The Fourier integral operators on Hardy spaces associated with Herz spaces},
url = {http://eudml.org/doc/196328},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Liu, Lixia
AU - Ma, Bolin
AU - Liu, Sanyang
TI - The Fourier integral operators on Hardy spaces associated with Herz spaces
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 1
SP - 271
EP - 287
AB - In this paper, it is proved that the Fourier integral operators of order $m$, with $-n < m \le -(n-1)/2$, are bounded from three kinds of Hardy spaces associated with Herz spaces to their corresponding Herz spaces.
LA - eng
KW - Fourier integral operator; Hardy spaces; Herz spaces; Fourier integral operator; Hardy space; Herz space
UR - http://eudml.org/doc/196328
ER -

References

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  2. Lu, S., Yang, D., 10.4064/sm-101-3-285-298, Stud. Math. 101 (1992), 285-298. (1992) MR1153785DOI10.4064/sm-101-3-285-298
  3. Lu, S., Yang, D., The decomposition of the weighted Herz spaces on R n and its applications, Sci. China Ser. A 38 (1995), 147-158. (1995) MR1338138
  4. Lu, S., Yang, D., The weighted Herz-type Hardy space and its applications, Sci. China Ser. A 38 (1995), 661-673. (1995) Zbl0832.42013MR1351232
  5. Marco, M. P., Silvia, S., 10.1017/S001309150500012X, Proc. Edinb. Math. Soc. 51 (2008), 443-463. (2008) MR2465918DOI10.1017/S001309150500012X
  6. Seeger, A., Sogge, C., Stein, E., 10.2307/2944346, Ann. Math. 134 (1991), 231-251. (1991) Zbl0754.58037MR1127475DOI10.2307/2944346
  7. Stein, E., Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press (1993). (1993) Zbl0821.42001MR1232192
  8. Yang, D., The real-variable characterizations of Hardy spaces H K p ( R n ) , Adv. Math. 24 (1995), 63-73. (1995) MR1334605
  9. Zhou, Y., 10.11650/twjm/1500405453, Taiwannse J. Math. 13 (2009), 983-996. (2009) Zbl1180.42009MR2526352DOI10.11650/twjm/1500405453

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